{"id":2653,"date":"2025-08-13T18:21:32","date_gmt":"2025-08-13T18:21:32","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/precalculus\/?post_type=chapter&#038;p=2653"},"modified":"2025-09-17T16:18:51","modified_gmt":"2025-09-17T16:18:51","slug":"systems-of-equations-and-inequalities-background-youll-need-4","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/precalculus\/chapter\/systems-of-equations-and-inequalities-background-youll-need-4\/","title":{"raw":"Systems of Equations and Inequalities: Background You'll Need 4","rendered":"Systems of Equations and Inequalities: Background You&#8217;ll Need 4"},"content":{"raw":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\r\n<ul>\r\n \t<li><span data-sheets-root=\"1\">Convert linear equations to slope-intercept form<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<p data-start=\"5266\" data-end=\"5357\">Slope\u2013intercept form is [latex]y=mx+b[\/latex]. Find this form by solving for [latex]y[\/latex].<\/p>\r\n\r\n<section class=\"textbox example\" aria-label=\"Example\">\r\n<p data-start=\"5371\" data-end=\"5409\">Convert each to [latex]y=mx+b[\/latex].<\/p>\r\n\r\n<ol data-start=\"5411\" data-end=\"5718\">\r\n \t<li data-start=\"5411\" data-end=\"5493\">\r\n<p data-start=\"5414\" data-end=\"5493\">[latex]3x+2y=8[\/latex]<\/p>\r\n<\/li>\r\n \t<li data-start=\"5495\" data-end=\"5589\">\r\n<p data-start=\"5498\" data-end=\"5589\">[latex]y-5=\\tfrac{4}{3}(x+6)[\/latex]<\/p>\r\n<\/li>\r\n \t<li data-start=\"5591\" data-end=\"5718\">\r\n<p data-start=\"5594\" data-end=\"5718\">[latex]2(y+1)=5(x-2)-3[\/latex]<\/p>\r\n<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"282806\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"282806\"]\r\n<ol>\r\n \t<li>[latex]4x-3y=12[\/latex]\r\n\r\n[latex]\r\n\\begin{align}\r\n4x-3y &amp;= 12 \\\\\r\n-3y &amp;= -4x+12 &amp;&amp; \\text{subtract }4x \\\\\r\ny &amp;= \\frac{4}{3}x-4 &amp;&amp; \\text{divide by }-3\r\n\\end{align}\r\n[\/latex]<\/li>\r\n \t<li>[latex]y+2=-2(x-3)[\/latex]\r\n\r\n[latex]\r\n\\begin{align}\r\ny+2 &amp;= -2(x-3) \\\\\r\ny+2 &amp;= -2x+6 &amp;&amp; \\text{distribute }-2 \\\\\r\ny &amp;= -2x+4 &amp;&amp; \\text{subtract }2\r\n\\end{align}\r\n[\/latex]<\/li>\r\n \t<li>[latex]2(y+1)=5(x-2)-3[\/latex]\r\n\r\n[latex]\r\n\\begin{align}\r\n2(y+1) &amp;= 5(x-2)-3 \\\\\r\n2y+2 &amp;= 5x-10-3 &amp;&amp; \\text{distribute} \\\\\r\n2y &amp;= 5x-15 &amp;&amp; \\text{subtract }2 \\\\\r\ny &amp;= \\frac{5}{2}x-\\frac{15}{2} &amp;&amp; \\text{divide by }2\r\n\\end{align}\r\n[\/latex]<\/li>\r\n<\/ol>\r\n[\/hidden-answer]\r\n\r\n<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm_question hide_question_numbers=1]312253[\/ohm_question]\r\n\r\n<\/section>","rendered":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\n<ul>\n<li><span data-sheets-root=\"1\">Convert linear equations to slope-intercept form<\/span><\/li>\n<\/ul>\n<\/section>\n<p data-start=\"5266\" data-end=\"5357\">Slope\u2013intercept form is [latex]y=mx+b[\/latex]. Find this form by solving for [latex]y[\/latex].<\/p>\n<section class=\"textbox example\" aria-label=\"Example\">\n<p data-start=\"5371\" data-end=\"5409\">Convert each to [latex]y=mx+b[\/latex].<\/p>\n<ol data-start=\"5411\" data-end=\"5718\">\n<li data-start=\"5411\" data-end=\"5493\">\n<p data-start=\"5414\" data-end=\"5493\">[latex]3x+2y=8[\/latex]<\/p>\n<\/li>\n<li data-start=\"5495\" data-end=\"5589\">\n<p data-start=\"5498\" data-end=\"5589\">[latex]y-5=\\tfrac{4}{3}(x+6)[\/latex]<\/p>\n<\/li>\n<li data-start=\"5591\" data-end=\"5718\">\n<p data-start=\"5594\" data-end=\"5718\">[latex]2(y+1)=5(x-2)-3[\/latex]<\/p>\n<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q282806\">Show Solution<\/button><\/p>\n<div id=\"q282806\" class=\"hidden-answer\" style=\"display: none\">\n<ol>\n<li>[latex]4x-3y=12[\/latex]\n<p>[latex]\\begin{align}  4x-3y &= 12 \\\\  -3y &= -4x+12 && \\text{subtract }4x \\\\  y &= \\frac{4}{3}x-4 && \\text{divide by }-3  \\end{align}[\/latex]<\/li>\n<li>[latex]y+2=-2(x-3)[\/latex]\n<p>[latex]\\begin{align}  y+2 &= -2(x-3) \\\\  y+2 &= -2x+6 && \\text{distribute }-2 \\\\  y &= -2x+4 && \\text{subtract }2  \\end{align}[\/latex]<\/li>\n<li>[latex]2(y+1)=5(x-2)-3[\/latex]\n<p>[latex]\\begin{align}  2(y+1) &= 5(x-2)-3 \\\\  2y+2 &= 5x-10-3 && \\text{distribute} \\\\  2y &= 5x-15 && \\text{subtract }2 \\\\  y &= \\frac{5}{2}x-\\frac{15}{2} && \\text{divide by }2  \\end{align}[\/latex]<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm312253\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=312253&theme=lumen&iframe_resize_id=ohm312253&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/section>\n","protected":false},"author":67,"menu_order":5,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":131,"module-header":"background_you_need","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/2653"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/users\/67"}],"version-history":[{"count":4,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/2653\/revisions"}],"predecessor-version":[{"id":4076,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/2653\/revisions\/4076"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/parts\/131"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/2653\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/media?parent=2653"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapter-type?post=2653"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/contributor?post=2653"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/license?post=2653"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}